# Quasi-Conformal Models and the Early Universe

## TL;DR

This paper explores quasi-conformal models derived from quadratic gravity as frameworks for inflation, highlighting two realizations involving fundamental and composite inflatons, with implications for observable cosmological parameters.

## Contribution

It introduces two novel inflation models based on UV complete quadratic gravity with Weyl invariance, providing analytical inflationary predictions and UV completions.

## Key findings

- Inflation models with quasi-conformal symmetry are consistent with current observations.
- Reheating can be efficiently achieved in these models.
- Tensor-to-scalar ratio predictions are below current observational bounds.

## Abstract

Extensions of the Standard Model and general relativity featuring a UV fixed point can leave observable implications at accessible energies. Although mass parameters such as the Planck scale can appear through dimensional transmutation, all fundamental dimension-4 operators can (at least approximately) respect Weyl invariance at finite energy. An example is the Weyl-squared term, whose consistency and observational consequences are studied. This quasi-conformal scenario emerges from the UV complete quadratic gravity and is a possible framework for inflation. We find two realizations. In the first one the inflaton is a fundamental scalar with a quasi-conformal non-minimal coupling to the Ricci scalar. In this case the field excursion must not exceed the Planck mass by far. An example discussed in detail is hilltop inflation. In the second realization the inflaton is a pseudo-Goldstone boson (natural inflation). In this case we show how to obtain an elegant UV completion within an asymptotically free QCD-like theory, in which the inflaton is a composite scalar due to new strong dynamics. We also show how efficient reheating can occur. Unlike the natural inflation based on Einstein gravity, the tensor-to-scalar ratio is well below the current bound set by Planck. In both realizations mentioned above, the basic inflationary formulae are computed analytically and, therefore, these possibilities can be used as simple benchmark models.